@gauthamnaidu -I know you are trying to help me, so no offence taken. First let us solve my laptop connection error, and then we will move to mobile screen sharing.
Coming back to the topic. I will write down the details in serial order
1) I have bought a Samsung 32F5500 which is a Smart TV.
2) I have not purchased any separate wireless modem/router etc.
3) From what I understand, this model has inbuilt wi-fi, so no need of any extra wi-fi modem/router (thats what I think).
In the Network option of the TV, there are following options -
a) Network Status (Check current network and Internet access.)
Network Status always shows Wireless Network disconnected. It shows some values in MAC Address. Other fields like IP Address, Subnet Mask, Gateway, DNS Server are always 0 0 0 0.
b) Network Settings (Set up your network to enjoy Smart Hub features like Internet browsing, home networking, feature updates and many more.)
This option searches for any nearby Wi-Fi networks. I made an ad-hoc profile in my Lenovo laptop which was detected as a separate Wi-Fi network on the TV. I also tried my friends HTC mobile which was detected by the TV (When the mobile was in Wi-Fi direct mode). BUT when I try to connect the devices with each other, it fails. It first asks for the necessary password (key). On entering the password(key), the TV shows as 'Connecting' and then after several seconds it shows 'Not able to connect'.
c) Wi-Fi Direct (When using Wi-Fi Direct, you can connect directly with other devices without using a wireless router.)
Because of this description I think/thought that my TV or mobile/laptop do not need to be connected to any other wireless router.
d) AllShare Settings (Share experiences by connecting to a variety of smart devices. Set up Content Sharing and Screen Mirroring.)
The Content Sharing option shows 'No Equipment Stored'. This is maybe because I haven't been able to connect the TV to any other device uptill now.
Screen Mirroring shows - [TV]Home - Ready for connection. To get started, launch AllShare Cast on your device.
e) Device Name ([TV] Home)
You can give the TV any name of your choice. I have kept the default [TV]Home.
Now I have downloaded and installed AllShare software on my Lenovo laptop. I have turned on the wi-fi of the laptop. I have made an ad-hoc connection on it which gets detected on the TV. I have turned ON the 'Allow Searching' Option on the AllShare settings of laptop. File Sharing has been turned ON in the Network and Sharing option. Still I am not able to connect them to each other.
How do we resolve this issue?